Identifying angle of departure of multi-antenna transmitters

ABSTRACT

A method for signal processing includes receiving at a given location at least first and second signals transmitted respectively from at least first and second antennas of a wireless transmitter. The at least first and second signals encode identical data using a multi-carrier encoding scheme with a predefined cyclic delay between the transmitted signals. The received first and second signals are processed, using the cyclic delay, in order to derive a measure of a phase delay between the first and second signals. Based on the measure of the phase delay, an angle of departure of the first and second signals from the wireless access point to the given location is estimated.

FIELD OF THE INVENTION

The present invention relates generally to wireless communicationsystems, and particularly to methods for localization based on wirelessnetwork signals.

BACKGROUND

Various techniques are known in the art for finding the location of amobile wireless transceiver, such as a cellular telephone. For example,nearly all cellular telephones now have a Global Positioning System(GPS) receiver, which derives location coordinates from signals receivedfrom geostationary satellites. Because of its dependence on weaksatellite signals, however, GPS works poorly, if at all, indoors and incrowded urban environments. Cellular networks are also capable oftriangulating telephone location based on signals received ortransmitted between the cellular telephone and multiple cellularantennas, but this technique is inaccurate and unreliable.

A number of methods have been proposed for indoor localization based onan existing wireless local area network (WLAN) infrastructure. One suchapproach is described, for example, by Kotaru et al., in “SpotFi:Decimeter Level Localization using WiFi,” published in SIGCOMM '15(London, UK, Aug. 17-21, 2015). According to the authors, SpotFicomputes the angle of arrival (AoA) of multipath components receivedfrom access points, and uses filtering and estimation techniques toidentify the AoA of a direct path between the localization target andthe access point.

As another example, U.S. Patent Application Publication 2009/0243932describes a method for determining the location of a mobile device. Themethod comprises transmitting a signal between a plurality of knownlocations and receiving the signal at a device of unknown location, suchas a mobile device. The signal may include multiple tones havingdifferent frequencies and resulting in sets of residual phasedifferences. The location of the mobile device may be determined usingthe known locations and the frequency and phase differences between thetransmitted tones. In one embodiment, OFDM signals may be used betweenan access point and mobile device to determine the location of themobile device.

As a further example, U.S. Patent Application Publication 2016/0033614describes a method of direction finding (DF) positioning involving mainlobe and grating lobe identification in a wireless communication networkis proposed. A receiver performs the DF algorithm on radio signalsassociated with multiple antennas over a first channel frequency andestimates a first set of DF solutions. The receiver performs the DFalgorithm on radio signals associated with multiple antennas over asecond channel frequency and estimates a second set of DF solutions. Thereceiver then identifies the correct DF solution (e.g., the main lobedirection) by comparing the first set of DF solutions and the second setof DF solutions.

Most current WLANs operate in accordance with the set of 802.11standards promulgated by the IEEE. Within this family, the IEEE802.11n-2009 standard (commonly referred to simply as “802.11n”) definesthe use of multiple antennas to increase data rates by means of“multiple input and multiple output” (MIMO) transmission and reception.MIMO enables the transmitter and receiver to coherently resolve moreinformation than would be possible using a single antenna, by means ofspatial division multiplexing (SDM), which spatially multiplexesmultiple independent data streams within one spectral channel ofbandwidth. The newer 802.11ac standard similarly supports MIMOtransmission, with a larger number of spatial streams and highertransmission rates than 802.11n.

SUMMARY

Some embodiments of the present invention that are described hereinbelowprovide improved methods for extracting directional information fromwireless access point signals, as well as devices and systems thatderive and make use of such information.

There is therefore provided, in accordance with an embodiment of theinvention, a method for signal processing, which includes receiving at agiven location at least first and second signals transmittedrespectively from at least first and second antennas of a wirelesstransmitter. The at least first and second signals encode identical datausing a multi-carrier encoding scheme with a predefined cyclic delaybetween the transmitted signals. The received first and second signalsare processed, using the cyclic delay, in order to derive a measure of aphase delay between the first and second signals. Based on the measureof the phase delay, an angle of departure of the first and secondsignals from the wireless access point to the given location isestimated.

In some embodiments, receiving the at least first and second signalsincludes receiving at least the first and second signals via a singlereceiving antenna, such as an omnidirectional antenna installed in amobile telephone.

Additionally or alternatively, the multi-carrier encoding schemeincludes an orthogonal frequency-domain multiplexing (OFDM) scheme. Insome embodiment, the transmitter is a wireless access point operating inaccordance with an 802.11 standard.

In the disclosed embodiments, processing the received first and secondsignals includes selecting at least two time-frequency bins in thereceived signals, and computing the measure of the phase delayresponsively to respective cyclic shifts of the selected bins. In someembodiments, selecting the at least two time-frequency bins includessampling first and second bins at a selected frequency within themulti-carrier encoding scheme in different, respective first and secondsymbols within a frame transmitted by the transmitter. In otherembodiments, selecting the at least two time-frequency bins includessampling first and second bins at different, respective first and secondfrequencies within the multi-carrier encoding scheme in a selectedsymbol within a frame transmitted by the transmitter.

In a disclosed embodiment, selecting the at least two time-frequencybins includes selecting first and second bins having antipodal phasesbased on standard cyclic shifts. Additionally or alternatively,computing the measure of the phase delay includes applying a lineartransformation to the signals extracted from the selected time-frequencybins.

In some embodiments, the first and second signals are transmitted inaccordance with a wireless communication standard that specifies a framestructure including a predefined preamble, and processing the receivedfirst and second signals includes selecting at least a part of thepreamble of a given frame for processing.

Additionally or alternatively, receiving and processing the at leastfirst and second signals include receiving and processing at least thefirst and second signals in a mobile station without establishing anassociation between the mobile station and the access point. In oneembodiment, receiving and processing at least the first and secondsignals includes receiving a beacon transmitted from the at least firstand second antennas in accordance with a predefined wirelesscommunication standard.

In some embodiments, the method includes receiving location informationwith respect to the wireless access point, and computing coordinates ofthe given location based on the received location information and theestimated angle of departure. Typically, computing the coordinatesincludes finding the coordinates based on the received locationinformation and the estimated angle of departure with respect to two ormore different wireless access points.

Additionally or alternatively, the method includes extracting anidentifier of the wireless access point from at least one of thereceived first and second signals. In one embodiment, the methodincludes reporting the identifier and the estimated angle of departureto a server, for incorporation into a map containing respectivelocations of multiple access points.

There is also provided, in accordance with an embodiment of theinvention, a method for mapping, which includes receiving reports, froma set of wireless communication devices at respective locations, ofrespective estimated angles of departure of signals received by thewireless communication devices from wireless access points. A map of thewireless access points is constructed based on the estimated angles ofdeparture.

In a disclosed embodiment, the wireless communication devices includemobile stations having a single antenna, while the wireless accesspoints each have multiple antennas, and the angles of departure areestimated based on a predefined cyclic delay between the signalstransmitted by the multiple antennas.

Additionally or alternatively, receiving the reports includes receivingfrom the wireless communication devices respective identifiers of thewireless access points and location coordinates of the wirelesscommunication devices where the signals were received.

In some embodiments, the method includes providing location informationfrom the map to one or more of the wireless communication devices. Inone embodiment, providing the location information includes identifyingposition coordinates of a wireless communication device based on anestimated angle of departure of signals received by the wirelesscommunication devices from a given access point and a location of thegiven access point in the map.

There is additionally provided, in accordance with an embodiment of theinvention, a wireless device, including a receive antenna, configured toreceive at a given location at least first and second signalstransmitted respectively from at least first and second antennas of awireless transmitter. The at least first and second signals encodeidentical data using a multi-carrier encoding scheme with a predefinedcyclic delay between the transmitted signals. Processing circuitry isconfigured to process the received first and second signals, using thecyclic delay, in order to derive a measure of a phase delay between thefirst and second signals, and to estimate, based on the measure of thephase delay, an angle of departure of the first and second signals fromthe wireless access point to the given location.

There is further provided, in accordance with an embodiment of theinvention, apparatus for mapping, including a memory and a processor,which is configured to receive reports, from a set of wirelesscommunication devices at respective locations, of respective estimatedangles of departure of signals received by the wireless communicationdevices from wireless access points, and to construct, in the memory, amap of the wireless access points based on the estimated angles ofdeparture.

The present invention will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is schematic, pictorial illustration of a system for wirelesscommunications and position finding, in accordance with an embodiment ofthe invention;

FIG. 2 is a diagram that schematically illustrates a coordinate frameused in deriving an angle of departure of wireless signals from anaccess point to a receiver, in accordance with an embodiment of theinvention;

FIG. 3 is a block diagram that schematically illustrates components of amobile receiver that are used in deriving coordinate information withrespect to wireless access points, in accordance with an embodiment ofthe invention; and

FIG. 4 is a schematic, pictorial illustration of components of thesystem of FIG. 1, illustrating a method for finding the position of amobile communication device, in accordance with an embodiment of theinvention.

DETAILED DESCRIPTION OF EMBODIMENTS Overview

Implementation of MIMO SDM schemes, such as those defined by the 802.11nstandard, requires a discrete antenna at both the transmitter and thereceiver for each spatial stream. Alternatively, the phases of thestreams can be adjusted to enable directional beamforming between theaccess point and mobile station, thus maximizing the signal at thereceiver. Many mobile devices, however, such as WiFi-enabledsmartphones, have only a single, omnidirectional antenna, and thuscannot themselves support MIMO or directional transmission.

In addition to actively forming beams toward the receiver, the 802.11nstandard also defines a scheme for preventing unintentional beamforming,which can occur if the data transmitted in the various spatial streamsinadvertently form correlated patterns, for example if the number ofstreams is smaller than the number of antennas. Unlike intentionalbeamforming, the pattern of lobes and nulls created by unintentionalbeamforming may not be oriented in such a way as to maximize the signalat the receiver, and thus can be detrimental to reception. To avoidunintentional beamforming, the 802.11n standard applies a cyclic delaydiversity (CDD) to offset the IFFT coded data stream from each antennaby a different constant, non-coherent delay. In the multi-carriermodulation system mandated by the 802.11n standard—known as orthogonalfrequency domain multiplexing (OFDM)—CDD is applied by adding apredefined cyclic shift in time which affects each carrier on eachantenna and is referred to equivalently as cyclic shift diversity (CSD).

Although CDD was introduced as a means for avoiding undesireddirectionality of multi-antenna wireless signals, embodiments of thepresent invention that are described herein exploit the CDD in receivedsignals for just the opposite purpose: to estimate the angularorientation of the access point transmitting the signals. This angularorientation is defined in terms of the angle of departure, i.e., theangle between the direction of the transmitted beam and the axis of thetransmitting access point (as defined by a line drawn through thelocations of the transmitting antennas). This sort of measurement ofangle of departure from the transmitter is in contrast to techniquesthat are known in the art for determining the angle of arrival ofsignals at the receiver. The angle of departure can be found, using thetechniques described herein, even when the signals from the transmittingantennas are received via a single receiving antenna, such as the sortof omnidirectional antenna that is commonly installed in mobiletelephones.

The embodiments of the present invention that are described hereinbelowspecifically provide methods for finding the angle of departure ofmultiple signals that are transmitted respectively from multipleantennas of a wireless access point and are received at a givenlocation. The transmitted signals encode, at least in part, identicaldata, with a predefined, per antenna, cyclic delay between thetransmitted signals. The data are typically defined and transmitted inaccordance with a known wireless communication standard, so that atleast a part of the data, as well as the cyclic delay, are predictable.For example, the 802.11 standards specify a frame structure including apredefined preamble, which can be selected for processing by thereceiver in the present context.

The receiver processes the received signals, using the known cyclicdelay, in order to derive a measure of the actual phase shift betweenthe signals. This phase shift, in turn, is indicative of the differencein path lengths that the signals traverse in reaching the receiver. Thespacing between the transmitting antennas is also known: typically λ/2(half the wavelength of the transmitted radio signals). Thus, based onthe measure of the phase shift, along with the known distance betweenthe antennas and the known amount of cyclic delay, it is possible toestimate the angle of departure of the signals from the wireless accesspoint to the location of the receiver.

In some embodiments, the signals are multi-carrier signals, such as thesort of OFDM signals that are used in the 802.11n standard, and thecyclic delay is thus implemented by applying different, respectivecyclic shifts to different antennas. In this case, the receiver is ableto estimate the phase shift between the antennas by properly selectingtwo time-frequency bins in the received signals, and computing themeasure of the phase shift using the respective cyclic shifts of bins astransmitted by the multiple antennas. By judicious selection of thebins, it is possible to compute the angle of departure by applying, forexample, a simple linear transformation to the extracted frequency bins.For this purpose, it is advantageous that the bins be chosen, based onthe cyclic delays defined by the applicable standard, so as to haveantipodal cyclic shifts.

The term “time-frequency bin,” as used in the context of the presentdescription and in the claims, means a sample of the received signal ata given, predefined frequency taken at a given, predefined time from thestart of a frame transmitted by the transmitter. Two time-frequency binscan be at the same frequency or different frequencies, and can occur atthe same or different times. In 802.11 OFDM transmissions, for example,a bin is defined in terms of frequency as one of N predefined complexnumbers used in data encoding prior to conversion to the time domain byInverse Fast Fourier Transform (IFFT), such as N=64 for 20 MHz 802.11OFDM. The input to the IFFT encoder in OFDM systems (which transformsfrequency-domain to time-domain signals) is a fixed-size collection ofcomplex numbers, each corresponding to a frequency bins.

Thus, in some embodiments (referred to as “time domain” embodiments),the two bins are defined by sampling a selected frequency within themulti-carrier encoding scheme at different, respective OFDM symbols,which are coded by different respective cyclic (time) shifts within aframe transmitted by the transmitter. In other embodiments (referred toas “frequency domain” embodiments), the two bins are defined by samplingtwo different frequencies within the multi-carrier encoding scheme atthe same selected OFDM symbol within a transmitted frame.

Another advantage of the present techniques is that they are capable ofreceiving and processing the access point signals in a mobile station,in order to measure the angle of departure, without establishing anassociation between the mobile station and the access point. In otherwords, the mobile station can simply capture signals silently, withouttransmitting signals back to the access point, and can analyze thesignals using the known, standard preamble structure and cyclic delay.The mobile station can apply this analysis, for example, to beacons thatare transmitted by an access point, in accordance with certain 802.11standards, even when there are no mobile stations communicating with theaccess point.

Alternatively, the mobile station can receive and analyze signals thatare directed to other mobile stations.

Although the angle of departure itself does not uniquely identify thelocation of the transmitting access point, multiple measurements ofangle of departure, from different, known receiver locations, can beused to find the access point location by triangulation. Thus, someembodiments of the present invention provide a method for mapping accesspoint locations by combining multiple measurements of angle of departuremade from different receiver locations. The signals transmitted by theaccess points also identify the access points (for example, byannouncing the Basic Service Set Identifier—BSSID), so that the identityof each access point can be associated with its location.

By the same token, when the locations of access points are known, it ispossible to find the location of a receiver by measuring the angles ofdeparture from two or more of these known access points to the receiver,using the techniques described above. Thus, once the locations of accesspoints in a certain area have been mapped, receivers, such as mobiletelephones, can find their own locations accurately within the areabased on the signals that they receive from the access points (evenwithout associating or otherwise communicating back with the accesspoints, as explained above). This sort of map of access points can thusbe used for accurate and convenient geo-location without dependence onGPS, for example in indoor and urban locations.

Although the embodiments described hereinbelow relate, for the sake ofconcreteness and clarity, specifically to 802.11 wireless access points,the principles of the present invention may similarly be applied,mutatis mutandis, to other sorts of multi-antenna transmitters thattransmit signals using multi-carrier encoding schemes. For example, inan alternative embodiment of the present invention, the receiver can beconfigured to measure angles of departure of multi-antenna cellular basestations that transmit OFDM signals in accordance with the applicablestandards. All such alternative implementations of the presentprinciples are considered to be within the scope of the presentinvention.

System Description

FIG. 1 is schematic, pictorial illustration of a system 20 for wirelesscommunications and position finding, in accordance with an embodiment ofthe invention. By way of example, FIG. 1 shows a typically indoor orurban environment, in which multiple access points 22, 24, 26, . . . ,are deployed, often by different WLAN proprietors independently of oneanother. Signals from the access points are received by mobile stations28, 30, . . . , which are operated by users 32 who are free to movearound within system 20. In the pictured embodiment, stations 28, 30, .. . , are shown as smartphones; but other sorts of mobile devices, suchas laptop and tablets computers, may be used in similar fashion and cansimilarly map angles of departure of access points 22, 24, 26, . . . ,as described hereinbelow.

Assuming access points 22, 24, 26, . . . , in system 20 are compliantwith the 802.11n standard, each access point has two or three antennas34, as shown in FIG. 1. The principles of the present invention aresimilarly applicable to 802.11ac access points, which may have an evengreater number of antennas. Mobile stations 28, 30, . . . , are eachassumed to have a single, omnidirectional antenna 36, although thetechniques described herein for mapping angles of departure cansimilarly be implemented by multi-antenna stations.

Mobile stations 28, 30, . . . , process signals received from antennas34 in order to estimate the angles of departure of the signals from therespective access points 22, 24, 26, . . . , as well as to extractidentifying information (such as the BSSID) with regard to each accesspoint. The mobile stations are able to perform these functions, asdescribed further hereinbelow, without necessarily associating with theaccess points.

On the other hand, mobile stations 28, 30, . . . , may associate withone or more of access points 22, 24, 26, . . . , for purposes ofInternet communications. Alternatively or additionally, the mobilestations may access the Internet via a cellular network or otherconnection. In any case, mobile stations 28, 30, . . . , communicate theangle-of-departure data and access point identification that theycollect via a network 38 to a mapping server 40. In addition, the mobilestations may communicate their current location coordinates to themapping server, as derived, for example, from GPS signals or from knownlocations of access points or base stations that are provided by server.This information may be collected and reported autonomously andautomatically by a suitable application program (“app”) running in thebackground on the mobile stations.

Server 40 typically comprises a general-purpose computer, comprising aprogrammable processor 42 and a memory 44. The functions of server 40that are described herein are typically implemented in software runningon processor 42, which may be stored on tangible, non-transitorycomputer-readable media, such as optical, magnetic or electronic memorymedia.

Based on the angle-of-departure information, access pointidentification, and location coordinates communicated over network 38 bymobile stations 28, 30, . . . , processor 42 builds up a map of accesspoint locations and orientations in memory 44. As greater numbers ofusers 32 download the application program and convey information toserver 40, the map will grow in both geographic extent and accuracy ofthe access point data, by a process of bootstrapping from an initialbase of seed information. On the basis of this map, server 40 can alsoprovide location and navigation information to users 32 via theapplication program running on their mobile stations, based on theaccess point signals received by the mobile stations at any given time.

Methods for Estimating Angle of Departure

FIG. 2 is a diagram that schematically illustrates a coordinate frameused in deriving an angle of departure of wireless signals from accesspoint 24 to mobile station 28, in accordance with an embodiment of theinvention. This particular pair of access point and mobile station isselected purely for convenience, and similar principles will apply toany given pair. Although access point 24 is shown as having two antennas34 (labeled Tx1 and Tx2), the same geometrical principles apply toaccess points having three or more antennas arranged in a linear array.

Antennas 34 define an array axis as the line passing through the basesof the antennas. The antennas are separated along the array axis by aknown distance d, which is typically designed to be a half wavelength,for example, λ/2=6.25 cm at the standard WLAN frequency of 2.4 GHz. Theangle of departure θ of the signals from antennas 34 to antenna 36 ofmobile station 28 is taken relative to the normal to the array axis, asshown in FIG. 2. Assuming the distance from access point 24 to mobilestation 28 to be considerably greater than d, there will be a differenceof d*sin θ in the path length from Tx1 to antenna 36 (referred to as Rx)relative to the path length from Tx2.

As an example, assuming the length of the path from Tx2 to Rx is 6.0000m, θ=30°, the slightly longer path from Tx1 to Rx will be 6.03125 m.This path difference translates into a 90° phase difference: Δϕ=dsin(π/6)=λ/2*½=λ/4. The propagation delay across 6 m is L/C=6 m/(0.3m/nsec)=20 nsec. Both paths, from Tx1 and Tx2, experience a linear phaseshift as a function of frequency, which is assumed to be zero atf₀=2.412 GHz and linearly grows to ϕ=(360° *20 nsec)/50 nsec=144° atf₁=2.432 GHz, wherein T=50 nsec= 1/20 MHz is given by the differenceB=20 MHz between the two frequencies. This linear phase shift of ϕ=144°between the two frequencies on both paths is in addition to the constantphase shift of 90° for the longer path at both frequencies, due to thepath length difference. (Actually, the phase shifts, both linear andconstant, are very slightly larger at 2.432 GHz, since the wavelength isvery slightly longer, but this effect can be neglected since B<<f₀.)

In addition, in accordance with the 802.11n standard, different cyclicshifts will be applied to the OFDM signals transmitted by Tx2 relativeto Tx1. A cyclic shift of Tcs<0 nanoseconds is equivalent to multiplyingfrequency bin k by

$e^{j\frac{2\pi}{N}{nk}},$wherein n=−B*Tcs, and N=64 is the number of frequency bins. It isadvantageous to choose the bins, as explained below, to have anantipodal relation, given the standard cyclic shifts, meaning that thereis a perfect 180° shift between Tx1 and Tx2 in the bin in question.Similarly, in three-antenna constellations, the standard specifiesdissimilar cyclic shifts that are to be applied on Tx2 and Tx3 relativeto Tx1. From the point of view of Rx antenna 36, there is no way ofknowing in advance which antenna 34 is Tx1 and which is Tx2 (or Tx3).There are two possible physical constellations of two antennas (2Tx):(1,2) and (2,1), i.e., the antenna array may be flipped over relative tothe receiver. There are six possible three-antenna (3Tx) constellations:(2,1,3), (1,2,3), (1,3,2) and their flip versions. In general, allpossible constellations are taken into account in computing the angle ofdeparture.

According to the 802.11 standards employing OFDM PHYs, data framestransmitted by access points have a preamble that includes a “ShortTraining Field” (STF) and a “Long Training Field” (LTF), containingpredefined sequences of symbols that are specified by the standards. The802.11a standard defined a frame format that is now referred to as the“legacy” format, which includes a legacy (L) preamble with L-STF andL-LTF fields. The 802.11n standard defines a new format, known as“high-throughput” (HT), with HT-STF and HT-LTF fields. Access pointsoperating in accordance with the 802.11n standard may transmit frames ineither legacy mode, HT-mode (“greenfield”), or mixed mode, in whichframes include both legacy and HT training fields.

The 802.11n standard defines the following cyclic shift values (Tcs) pertransmitting antenna in the legacy and HT preambles (see Tables 20-9 and20-10 in the standard). These Tcs values in turn give rise to differentsubcarrier phase shifts, in accordance with the formula presented above

$\left( e^{j\frac{2\pi}{N}{nk}} \right),$for different time-frequency bins (n,k), with N=64 for 20 MHz channels:

TABLE 1 Legacy HT Tcs n k = 0 k = 4 k = 8 k = 16 Tx1 Tx1 0 0 0 0 0 0 Tx2— −100 2 0 π/4 π/2 π Tx3 Tx3 −200 4 0 π/2 π 2π — Tx2 −400 8 0 π 2π 4π

Antipodality between the selected bins, i.e. 180° phase shift followingCDD, provides the greatest Euclidean distance between the signals, thusenhancing noise immunity.

Embodiments of the present invention use two different methods toachieve antipodality:

(1) In the time domain method, a bin k0 in a legacy OFDM symbol and abin k0 in an HT symbol are selected at a certain fixed frequency.

(2) In the frequency domain method, two bins are chosen at differentfrequencies in a single OFDM symbol, for example a legacy OFDM symbol.

Antipodality provides the best Euclidean distance for noise immunity.

Projecting the path differences between the antennas back to thetransmitter antenna feeds, the phases of the two signals are (0, 0), orequivalently (e^(j0),e^(jθ)) in complex form, for the two-antenna case,and (−θ, 0, θ), equivalent to (e^(−jθ),e^(j0),e^(jθ)), in thethree-antenna case, wherein θ is the angle of departure as shown in FIG.2. Projecting post-IFFT encoder cyclic shifts onto the transmitter“frequency domain,” for judiciously chosen shifts and bins, gives aphase of either 0 or 180°. The two or more rays emitted from thetransmitter are superimposed at the single antenna of the receiver.

The combined effect of path propagation, cyclic shift and superpositionis a signal of the form

1±e^(jθ) for two antennas. For three antennas, there are two physicallydifferent cases: an anti-symmetrical case (“case I”) and a symmetricalcase (“case II”), yielding a combined signal of e^(−jθ)+1±e^(jθ) ore^(−jθ)±1+e^(jθ), respectively.

Returning now to the specific two-antenna example shown in FIG. 2 andthe path phase differences calculated above, selecting natural exponentsof jπ in the time domain (as indicated by the “π” entries in Table 1),the phase shifts between the signals received by antenna 36 fromantennas 34 Tx1 and Tx2 at f₀=2.412 MHz in the L-LTF and HT-LTF fieldsof a mixed-mode frame will be as follows:

Tx L-LTF HT-LTF 1  0° 0° 2 −90° −90° + 180°In the above example, the difference of −90° in the antenna pathsapplies only to Tx2, while 180° is due to the cyclic shift, which isapplied only to HT-LTF on Tx2.

The phases of the corresponding received signals at f₁=2.432 MHz willbe:

Tx L-LTF HT-LTF 1  0° + 144° 0° + 144° 2 −90° + 144° −90° + 144° + 180°Here the additional 144° is due to the phase shift across the commonpath from transmitter to receiver, applied to all time slots.

Upon receiving the signals from the transmitted L-LTF bins in thefrequency domain case, or both HT-LTF and L-LTF bins in the time domaincase, from access point 24, mobile station 28 computes the phasedifference between the Tx1 path and the Tx2 path. This difference isindicative, in turn, of the angle of departure of the signals fromaccess point 24, as illustrated in FIG. 2. Computational methods thatcan be used to derive the angle of departure in this manner aredescribed hereinbelow.

FIG. 3 is a block diagram that schematically illustrates components ofmobile station 28 that are used in deriving coordinate information withrespect to wireless access points, in accordance with an embodiment ofthe invention. The description that follows assumes that mobile station28 has a single antenna 36, which receives the signal streamstransmitted by two or three antennas 34 of an access point, but theprinciples of this embodiment may similarly be applied, mutatismutandis, by a multi-antenna receiver in order to achieve path diversitywhile measuring the same angle of departure. As explained above, theanalysis performed by mobile station relies on the fact that the signalstransmitted from the different antennas encode identical data in theframe preambles, with a predefined cyclic delay between the transmittedsignals as defined by the 802.11n standard.

A front end (FE) circuit 50 in mobile station 28 amplifies, filters, anddigitizes the signals received by antenna 36, as is known in the art,and passes the resulting digital samples to digital processing circuitry52. A fast Fourier transform (FFT) circuit 54 in circuitry 52 dividesthe incoming signal into time-frequency bins (n,k), wherein eachfrequency corresponds to a different OFDM subcarrier, and the phase ofthe signal component in each bin is determined by the data value that itencodes. A media access control (MAC) processing circuit 56 extractsdata from the frame header, including the BSSID that identifies theaccess point that transmitted the frame. Circuits 50, 54 and 56, as wellas other components of digital processing circuitry 52, are conventionalelements of 802.11 receivers, such as those installed in WiFi-capablesmartphones that are known in the art for purposes of data reception andtransmission. Other elements of the receiver that are not essential foran understanding of the present invention are omitted for the sake ofbrevity.

The signal complex frequency bins generated by FFT circuit 54 are inputto an angle estimation block, which includes a bin selector 58 and atransformation module 60 and an angle differentiator 61. These elementsconvert the complex values into an estimated angle of departure. Theyare typically implemented in software running on a programmableprocessor in mobile station 28. This software may be a part of anapplication program running on the mobile station, as described above,along with other functions performed by a processor already present inthe mobile station. This program may be stored in tangible,non-transitory computer-readable media, such as optical, magnetic, orelectronic memory media. Alternatively or additionally, at least a partof the angle estimation functions described herein may be performed byin dedicated or programmable hardware logic.

Bin selector 58 selects a pair of time-frequency bins, (n₁,k₁) and(n₂,k₂), to be extracted from the preambles of the received signals, andextracts the corresponding phase values. For each bin, the bin selectorcomputes the complex vectors, y_(i), between the respective signalsreceived from two of antennas 34. The two selected complex bins define acomplex vector

${\overset{->}{y} = \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}},$which is input to complex transformation module 60. Although any pair ofbins can be chosen for this purpose, it is advantageous to choose apair, based on the known cyclic shifts, in which the relative phasedelay can be linearly related to the angle of departure of the signalstransmitted from the access point across a broad span of angles.

The choice of the difference between the frequencies of the bins,Δk=k₁−k₂, involves a tradeoff between thermal noise, which can besignificant for small Δk, and channel deviations and sensitivity to timeof flight, which grow as Δk grows. The numerical examples provided hereassume cyclic shifts are chosen so as to achieve antipodality. Thefrequency response of the wireless channel between the access point andthe receiver is not linear in phase, due, for example, to the impact ofreflections. In general, the larger the value of Δk, the larger theadded error to the estimated phase delay due to variation in the channelresponse. In the case of 802.11n signals with 20 MHz bandwidth, forexample, a reasonable tradeoff is achieved with Δk=8, which reflects afrequency difference of 8/64*20 MHz=2.5 MHz. The following frequencycombinations (k₁,k₂) satisfy this criterion: (0,8), (16,8), (16,24),(32,40), (48,40), (48,56) and (0,56). Since the HT-LTF does not populatefrequencies 0 and 32, however, the combinations (0,8) and (32,40) arenot applicable. Other bin pair patterns of the form (k₀,k₀₊₈) can beused, as well, so long as both preamble bins carry energy.

Transformation module 60 applies a linear transformation T in order toconvert the complex input vector into an output vector: {right arrowover (x)}=T{right arrow over (y)}. The purpose of this transformation isto generate the pair of values

$\overset{->}{x} = \begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}$such that the phases of x₁ and x₂ can be easily extracted and subtractedby differentiator 61 to give the estimated angle of departure:{circumflex over (θ)}=arg(x₂)−arg(x₁).

For example, in the case of two antenna elements the followingtransformation provides linear estimation of the output vector:

$\overset{->}{x} = {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}\overset{->}{y}}$

{right arrow over ( )}[ ]{right arrow over ( )} Mobile station 28transmits the estimated angle of departure, along with the BSSIDextracted by MAC processing circuit 56, via network 38 to server 40. Inaddition, mobile station 28 transmits information regarding the currentlocation of the mobile station to server 40, as provided by a locationresolution module 62. Module 62 may comprise, for example, a GPSreceiver, which outputs location coordinates based on satellite signals.Additionally or alternatively, module 62 may be implemented in softwarerunning on a processor in processing unit 52 and may compute currentlocation coordinates of mobile station 28 based on signals received fromother, known access points that have already been mapped by server 40,or other sources. In any case, server 40 receives the estimated angle ofdeparture data together with the current, estimated location of themobile station. The server is thus able to find the actual location ofaccess point 24 based on multiple angle measurements reported by mobilestation 28 (or by multiple mobile stations) from different locations.

Examples of Angle of Departure Estimation

Two Antennas, Mixed Format (MF, HT with Legacy Compliance) Mode

A plausible “time domain” choice of a time-frequency pair of bins in thecase of two transmitting antennas is (n,k)=(4,k₀) and (8,k₀), wherein k₀is any element in the set {8,24,40,56}. This choice providesantipodality, i.e., the phase contribution of the cyclic shift is either0 or 180°. The time bin n=4 is in the legacy preamble (L-LTF), while binn=8 (400 nsec*20 MHZ) is in the HT preamble (HT-LTF). (The bin n=4corresponds to 200 ns*20 MHZ, wherein 200 ns is the CDD mandated by thestandard, and 20 MHz is a typical 802.11 OFDM channel bandwidth. Channelbandwidths of 40 MHz, 80 MHz and 160 MHz are possible, as well.) Thisselection of bins generates antipodal phases between the two readings,i.e., summing (or equivalently, subtracting) the signals from the twoantennas in the measured bins gives the complex vector

$\overset{->}{y} = {\begin{bmatrix}{1 + e^{j\;\phi}} \\{1 - e^{j\;\phi}}\end{bmatrix}.}$

Transformation module 60 transforms this vector linearly into

$\overset{->}{x} = {{\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}\overset{->}{y}} = {{2\begin{bmatrix}1 \\e^{{- j}\;\phi}\end{bmatrix}}.}}$Hence the estimated angle of departure is {circumflex over(θ)}=arg(x₂)−arg(x₁)=ϕ.Three Antennas, MF Mode

Case I

The same time-frequency bins are selected as in the previous example,assuming that antennas 34 are arrayed along the axis of the transmittingaccess point in the order (1,3,2) or (2,1,3) or in the flip versions ofthese orders. In all of these cases, extraction of the phases from thepairs of bins (n,k)=(4,k₀) and (8,k₀) will yield the following complexvector:

$\overset{->}{y} = {\begin{bmatrix}{e^{{- j}\;\phi} + 1 + e^{j\;\phi}} \\{e^{{- j}\;\phi} + 1 - e^{j\;\phi}}\end{bmatrix}.}$The reason for this result is that antennas Tx1 and Tx3 have the samecyclic shift (n=4), while Tx2 has a cyclic shift of n=8, which for theabove set of values of k₀ results in a complete 180° rotation.

Applying the same transformation in module 60 as in the precedingexample results in the angular vector:

$\overset{->}{x} = {{\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}\overset{->}{y}} = {{2\begin{bmatrix}{1 + e^{{- j}\;\phi}} \\e^{j\;\phi}\end{bmatrix}} = {{e^{{- j}\frac{\;\phi}{2}}\begin{bmatrix}{e^{{- j}\frac{\;\phi}{2}} + e^{j\frac{\;\phi}{2}}} \\e^{j\frac{\;{3\phi}}{2}}\end{bmatrix}} = {{e^{{- j}\frac{\;\phi}{2}}\begin{bmatrix}{\cos\frac{\phi}{2}} \\e^{j\frac{\;{3\phi}}{2}}\end{bmatrix}}.}}}}$Hence,

$\hat{\theta} = {{{\arg\left( x_{2} \right)} - {\arg\left( x_{1} \right)}} = {\frac{3\phi}{2}.}}$

Case II

The array constellation of (1,2,3) and its flip case result in thefollowing phase vector:

$\overset{->}{y} = {\begin{bmatrix}{e^{{- j}\;\phi} + 1 + e^{j\;\phi}} \\{e^{{- j}\;\phi} - 1 + e^{j\;\phi}}\end{bmatrix}.}$In this case, module 60 applies the transformation

${\overset{->}{x} = {\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}\overset{->}{y}}},$which generates a non-linear S-curve of angle as a function of phase,spanning

$\frac{3\pi}{2}.$The curve is symmetrical around the boresight direction (i.e., thedirection perpendicular to the array axis shown in FIG. 2). In otherwords, for a given phase delay, the angle of departure has a unique,corresponding absolute value, with a sign that can be either positive ornegative.

Similar results can be obtained by a frequency domain analysis: Whenusing different frequency bins of the HT-LTF, the signal from eachantenna is cyclically shifted by a different delay, as shown in Table 1above. The case of Δk=8 is identical in phase shifts to thethree-antenna time-domain case analyzed above, with phase shifts of 0and π:

$e^{j\frac{2\pi}{N}{nk}}$ n Tcs k = 16 k = 8 e^(−jθ) 0    0 1 1 e^(j0) 8−400 1 1 e^(+jθ) 4 −200 1 −1

The bins (n,k)=(8,0) and (n,k)=(8,8) result in the same phasecombination as the above time domain case I: {right arrow over (y)}=

$\begin{bmatrix}{e^{{- j}\;\phi} + 1 + e^{j\;\phi}} \\{e^{{- j}\;\phi} + 1 - e^{j\;\phi}}\end{bmatrix},$with the same angle estimator as above. The resultant estimator isperfectly linear with output span of 3π, and a full span set at a slantof π.Three Antennas, Legacy Mode

In legacy mode, access point 24 periodically transmits beacons,typically roughly every 100 msec. Therefore, mobile station 28 canadvantageously receive and process these beacons to find the angle ofdeparture of access point 24, since the beacons are transmittedirrespectively of any association by a mobile station. Furthermore,because beacons are always sent with a bandwidth of 20 MHz, the receivercan be agnostic to the actual bandwidth that is used for data (which maybe 20, 40, 80 or 160 MHz, for example).

In the case of the L-LTF, the cyclic shift relative to Tx1 is 100 ns forTx2 and 200 ns for Tx3, respectively:

n Tcs k = 0 k = 16 e^(−jθ) 0 0 1 1 e^(j0) 2 −100 1 −1 e^(+jθ) 4 −200 1 1Hence for Δk=16 (double the frequency offset Δk=8 used above for HT),the phase pattern is identical to Case I above.Antenna Constellation

The transformations described above, when applied by transformationmodule 60, give estimates of the angle of departure but do notnecessarily resolve the actual configuration of the transmit antennaconstellation. Digital processing unit 52 may therefore apply anadditional, parallel estimator in order to differentiate between one,two and three transmitting antennas, and in the case of three antennas,to differentiate between Case I and Case II defined above.

In one embodiment of the present invention, transformation module 60extracts the antenna constellation by applying a different lineartransformation in the time domain: No transformation in thethree-antenna Case II results in an output difference of either 0 or πat any direction of departure. In the case of two antennas, thefollowing transformation results in an output difference of either 0 orπ at any direction of departure:

$\overset{->}{x} = {\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}{\overset{->}{y}.}}$

A second method to ascertain the number of antenna elements and theirlinear formation is based on using a plurality of time-frequency pairs(n, k), all of which provide an unbiased time of departure estimation.For example, in the frequency domain method described above with bins(n,k₀) and (n,k₀₊₈), values of k₀=0, 1, 2, . . . , 55 can be used forbins bearing energy n=4 and N=64.

It is not generally possible to determine whether in the two-antennacase, the antenna order is (1,2) or (2,1). The ambiguity of order can bereadily resolved, however, by making multiple measurements of angle ofdeparture, using the same receiver or multiple different receivers atdifferent locations.

Three-antenna transmitters can readily be distinguished from two-antennatransmitters using the techniques described above: Since differentcyclic delays are used in two- and in three-antenna devices, receptionand processing of a single MF packet is sufficient to apply a crosscheckbetween the above time-domain and frequency-domain estimations. Only thecorrect antenna estimator (two-antenna or three-antenna) will give thesame results for both the time-domain and frequency-domain estimations.

System Applications

FIG. 4 is a schematic, pictorial illustration of components of thesystem of FIG. 1, illustrating a method for finding the position of amobile communication device 70, in accordance with an embodiment of theinvention. This method assumes that the respective location coordinatesand BSSIDs of access points 22, 24 and 26 have already been mapped byserver 40, on the basis of measurements of angle of departure that weremade previously by other mobile stations and/or other input data.

Device 70 receives multi-antenna signals from each of access points 22,24 and 26 and extracts the respective angle of departure for each accesspoint, labeled θ₁, θ₂, and θ₃ in the figure, using the techniquesdescribed above, along with the respective BSSIDs. Device 70 reportsthese findings via network 38 to server 40, which returns correspondinglocation coordinates. The server may return the location coordinates ofthe access points, in which case device 70 can triangulate its ownposition based on these coordinates and the measured angles ofdeparture. Alternatively or additionally, device 70 conveys the valuesof the angles of departure that it has estimated to server 40, whichthen returns the location coordinates of device 70.

In order to provide these sorts of location data to device 70, server 40builds up and maintains a map of access point locations and orientationsin memory 44 (FIG. 1). Typically, the map is built up on the basis ofmeasurements of angle of departure, BSSID, and device location that arereported by mobile stations in various areas. Server 40 may use theinformation reported by device 70, as illustrated in FIG. 4, not only toprovide location information to device 70, but also to extend and refinethe map maintained by the server. In this manner, for example, theserver can continually add new access points to the map and can refinethe accuracy of the access point locations and orientations in the map.

Server 40 can build this access point map without requiring anycooperation by operators of the access points. Similarly once users ofmobile devices have installed the mapping application, their mobiledevices can measure and report access point data to the serverautonomously, without active user involvement. The more users subscribeto the mapping application, the more extensive and more accurate will bethe resulting maps and access point locations that they provide.

It will be appreciated that the embodiments described above are cited byway of example, and that the present invention is not limited to whathas been particularly shown and described hereinabove. Rather, the scopeof the present invention includes both combinations and subcombinationsof the various features described hereinabove, as well as variations andmodifications thereof which would occur to persons skilled in the artupon reading the foregoing description and which are not disclosed inthe prior art.

The invention claimed is:
 1. A method for signal processing, comprising:receiving at a given location at least first and second signalstransmitted respectively from at least first and second antennas of awireless transmitter, the at least first and second signals encodingidentical data using a multi-carrier encoding scheme with a predefinedcyclic delay between the transmitted signals; processing the receivedfirst and second signals, using the cyclic delay, in order to derive ameasure of a phase delay between the first and second signals, whereinprocessing the received first and second signals comprises selecting atleast two time-frequency bins in the received signals, and computing themeasure of the phase delay responsively to respective cyclic shifts ofthe selected bins; and based on the measure of the phase delay,estimating an angle of departure of the first and second signals fromthe wireless access point to the given location.
 2. The method accordingto claim 1, wherein receiving the at least first and second signalscomprises receiving at least the first and second signals via a singlereceiving antenna.
 3. The method according to claim 2, wherein thesingle receiving antenna is an omnidirectional antenna installed in amobile telephone.
 4. The method according to claim 1, wherein themulti-carrier encoding scheme comprises an orthogonal frequency-domainmultiplexing (OFDM) scheme.
 5. The method according to claim 4, whereinthe transmitter is a wireless access point operating in accordance withan 802.11 standard.
 6. The method according to claim 1, whereinselecting the at least two time-frequency bins comprises sampling firstand second bins at a selected frequency within the multi-carrierencoding scheme in different, respective first and second symbols withina frame transmitted by the transmitter.
 7. The method according to claim1, wherein selecting the at least two time-frequency bins comprisessampling first and second bins at different, respective first and secondfrequencies within the multi-carrier encoding scheme in a selectedsymbol within a frame transmitted by the transmitter.
 8. The methodaccording to claim 1, wherein selecting the at least two time-frequencybins comprises selecting first and second bins having antipodal phasesbased on standard cyclic shifts.
 9. The method according to claim 1,wherein computing the measure of the phase delay comprises applying alinear transformation to the signals extracted from the selectedtime-frequency bins.
 10. The method according to claim 1, wherein thefirst and second signals are transmitted in accordance with a wirelesscommunication standard that specifies a frame structure including apredefined preamble, and wherein processing the received first andsecond signals comprises selecting at least a part of the preamble of agiven frame for processing.
 11. The method according to claim 1, whereinreceiving and processing the at least first and second signals comprisereceiving and processing at least the first and second signals in amobile station without establishing an association between the mobilestation and the access point.
 12. The method according to claim 1, andcomprising receiving location information with respect to the wirelessaccess point, and computing coordinates of the given location based onthe received location information and the estimated angle of departure.13. The method according to claim 1, and comprising extracting anidentifier of the wireless access point from at least one of thereceived first and second signals.
 14. A method for signal processing,comprising: receiving at a given location at least first and secondsignals transmitted respectively from at least first and second antennasof a wireless transmitter, the at least first and second signalsencoding identical data using a multi-carrier encoding scheme with apredefined cyclic delay between the transmitted signals; processing thereceived first and second signals, using the cyclic delay, in order toderive a measure of a phase delay between the first and second signals,wherein receiving and processing the at least first and second signalscomprise receiving and processing at least the first and second signalsin a mobile station without establishing an association between themobile station and the access point, and wherein receiving andprocessing at least the first and second signals comprises receiving abeacon transmitted from the at least first and second antennas inaccordance with a predefined wireless communication standard; and basedon the measure of the phase delay, estimating an angle of departure ofthe first and second signals from the wireless access point to the givenlocation.
 15. A method for signal processing, comprising: receiving at agiven location at least first and second signals transmittedrespectively from at least first and second antennas of a wirelesstransmitter, the at least first and second signals encoding identicaldata using a multi-carrier encoding scheme with a predefined cyclicdelay between the transmitted signals; receiving location informationwith respect to the wireless access point, and computing coordinates ofthe given location based on the received location information and theestimated angle of departure, wherein computing the coordinatescomprises finding the coordinates based on the received locationinformation and the estimated angle of departure with respect to two ormore different wireless access points; processing the received first andsecond signals, using the cyclic delay, in order to derive a measure ofa phase delay between the first and second signals; and based on themeasure of the phase delay, estimating an angle of departure of thefirst and second signals from the wireless access point to the givenlocation.
 16. A method for signal processing, comprising: receiving at agiven location at least first and second signals transmittedrespectively from at least first and second antennas of a wirelesstransmitter, the at least first and second signals encoding identicaldata using a multi-carrier encoding scheme with a predefined cyclicdelay between the transmitted signals; processing the received first andsecond signals, using the cyclic delay, in order to derive a measure ofa phase delay between the first and second signals; based on the measureof the phase delay, estimating an angle of departure of the first andsecond signals from the wireless access point to the given location;extracting an identifier of the wireless access point from at least oneof the received first and second signals; and reporting the identifierand the estimated angle of departure to a server, for incorporation intoa map containing respective locations of multiple access points.
 17. Awireless device, comprising: a receive antenna, configured to receive ata given location at least first and second signals transmittedrespectively from at least first and second antennas of a wirelesstransmitter, the at least first and second signals encoding identicaldata using a multi-carrier encoding scheme with a predefined cyclicdelay between the transmitted signals; and processing circuitry, whichis configured to process the received first and second signals, usingthe cyclic delay, in order to derive a measure of a phase delay betweenthe first and second signals, and to estimate, based on the measure ofthe phase delay, an angle of departure of the first and second signalsfrom the wireless access point to the given location, wherein theprocessing circuitry is configured to select at least two time-frequencybins in the received signals, and to compute the measure of the phasedelay responsively to respective cyclic shifts of the selected bins. 18.The device according to claim 17, wherein the receive antenna comprisesa single antenna, which receives both the first and second signals. 19.The device according to claim 18, wherein the single antenna is anomnidirectional antenna, and the device is a mobile telephone.
 20. Thedevice according to claim 17, wherein the multi-carrier encoding schemecomprises an orthogonal frequency-domain multiplexing (OFDM) scheme. 21.The method according to claim 20, wherein the transmitter is a wirelessaccess point operating in accordance with an 802.11 standard.
 22. Thedevice according to claim 17, wherein the at least two time-frequencybins comprise first and second bins at a selected frequency within themulti-carrier encoding scheme, occurring in different, respective firstand second symbols within a frame transmitted by the transmitter. 23.The device according to claim 17, wherein the at least twotime-frequency bins comprise first and second bins at different,respective first and second frequencies within the multi-carrierencoding scheme, occurring in a selected symbol within a frametransmitted by the transmitter.
 24. The device according to claim 17,wherein the at least two time-frequency bins are selected so as to haveantipodal phases based on standard cyclic shifts.
 25. The deviceaccording to claim 17, wherein the processing circuitry is configured toapply a linear transformation to the signals extracted from the selectedtime-frequency bins in order to estimate the angle of departure.
 26. Thedevice according to claim 17, wherein the first and second signals aretransmitted in accordance with a wireless communication standard thatspecifies a frame structure including a predefined preamble, and whereinthe processing circuitry is configured to select at least a part of thepreamble of a given frame for processing.
 27. The device according toclaim 17, wherein the processing circuitry is configured to receive andprocess at least the first and second signals without establishing anassociation with the access point.
 28. The device according to claim 17,wherein the processing circuitry is configured to receive locationinformation with respect to the wireless access point, and to computecoordinates of the given location based on the received locationinformation and the estimated angle of departure.
 29. The deviceaccording to claim 17, wherein the processing circuitry is configured toextract an identifier of the wireless access point from at least one ofthe received first and second signals.
 30. A wireless device,comprising: a receive antenna, configured to receive at a given locationat least first and second signals transmitted respectively from at leastfirst and second antennas of a wireless transmitter, the at least firstand second signals encoding identical data using a multi-carrierencoding scheme with a predefined cyclic delay between the transmittedsignals; and processing circuitry, which is configured to process thereceived first and second signals, using the cyclic delay, in order toderive a measure of a phase delay between the first and second signals,and to estimate, based on the measure of the phase delay, an angle ofdeparture of the first and second signals from the wireless access pointto the given location, wherein the processing circuitry is configured toreceive and process at least the first and second signals withoutestablishing an association with the access point, and wherein the firstand second signals comprise a beacon transmitted from the at least firstand second antennas in accordance with a predefined wirelesscommunication standard.
 31. A wireless device, comprising: a receiveantenna, configured to receive at a given location at least first andsecond signals transmitted respectively from at least first and secondantennas of a wireless transmitter, the at least first and secondsignals encoding identical data using a multi-carrier encoding schemewith a predefined cyclic delay between the transmitted signals; andprocessing circuitry, which is configured to process the received firstand second signals, using the cyclic delay, in order to derive a measureof a phase delay between the first and second signals, and to estimate,based on the measure of the phase delay, an angle of departure of thefirst and second signals from the wireless access point to the givenlocation; wherein the processing circuitry is configured to receivelocation information with respect to the wireless access point, and tocompute coordinates of the given location based on the received locationinformation and the estimated angle of departure, and wherein theprocessing circuitry is configured to compute the coordinates based onthe received location information and the estimated angle of departurewith respect to two or more different wireless access points.
 32. Awireless device, comprising: a receive antenna, configured to receive ata given location at least first and second signals transmittedrespectively from at least first and second antennas of a wirelesstransmitter, the at least first and second signals encoding identicaldata using a multi-carrier encoding scheme with a predefined cyclicdelay between the transmitted signals; and processing circuitry, whichis configured to process the received first and second signals, usingthe cyclic delay, in order to derive a measure of a phase delay betweenthe first and second signals, and to estimate, based on the measure ofthe phase delay, an angle of departure of the first and second signalsfrom the wireless access point to the given location, wherein theprocessing circuitry is configured to extract an identifier of thewireless access point from at least one of the received first and secondsignals, and wherein the processing circuitry is configured to reportthe identifier and the estimated angle of departure to a server, forincorporation into a map containing respective locations of multipleaccess points.